I think the original idea was that they were using one of the (now retired) metal masters (the moulds for the LP). It makes sense - "you've sold so many records that our master has worn out, so have the old one as an award".

Then later as the convention of the awards stuck, they just metallized an LP.

Yes, they're negatives of the printed LP; they can be played but require a special needle. There was a video where Jack White (of The White Strips) bought an old Elvis master and explained how to play it.

I never really thought about the awards and what they mean in an era where everything would have been digital (and that's a long time now). Of course a lot of artists do commission LPs these days (though has that gone out of fashion? - there was a resurgence there in the 2010's at least) so you can imagine that the masters could be handed out as souvenirs.

Worn records can play. The quality wouldn't be as good.

It's the master, the mold, the negative. It's an inverted record.

Just play it in reverse then ;)

And with a forked needle - not actually a joke.